The terms in the cost function related to the (small) constants \(\mu _\mathbf {x}, \mu _\mathbf {a} \in \mathbb {R}_{\ge 0}\)  are regularization terms to remedy the effects of overfitting [1]}. If multiple or even infinitely many minima exist, these regularization terms keep the magnitudes of the computed, minimizing state and parameter values relatively small. The selection of suitable regularization constants is an open problem, and a topic for future work.
